Classes of smoothed Weyl symbols

We propose a new class of time frequency (TF) symbols covariant to time shi fts and frequency shifts on a random process. The new TF symbols are useful for analyzing linear time-varying systems or nonstationary random processe s, and they are defined as TF-smoothed versions of the narrowband Weyl symb ol. We derive kernel constraints for the new TF symbols to satisfy the unit arity property and the quadratic form, We also propose a new class of TF sy mbols covariant to time shifts and scale changes on a random process. These new TF symbols can be interpreted as affine-smoothed versions of the narro wband Weyl symbol or of the wideband P-o-Weyl symbol.